Most of us have gone through breakups/splits with partners, and even though relationships and their endings often have different lengths, reasons for fading of love, and sometimes "off-and-on" types of situations, there are a few things that remain static, and that pretty much boils down to what you take away from the relationship after it's over.
Whose fault was it?
When a relationship ends, it's usually for a good reason. In cases where someone was cheating, lied about something significant, or stole something from you, it's easy to find blame in the other person. However, not every relationship ends that way. I find that more often than not, people end up in sort of this breakup "grey area" where they're not really sure whose fault it was, it just ended. Sometimes that's okay, too.
The critical thing you do here when the relationship is over and you've had your potential grief period, is evaluate this situation. Could it be your own fault the relationship ended? Was it solely the other person at fault? Maybe it was a little bit of both?
Rather than instantly blaming the other person for the relationship's failure and harboring anger or sadness towards them, sometimes you have to look within, and see if you've made some mistakes as well, leading to the downfall. Take a step back from the situtation, and realize that you're not perfect, no human is. Everyone takes misteps in their life, and knowing where and how you mistepped is the key to learning from the experience. If you lived with your partner, did you do enough to help out around the house/apartment? If you didn't, did you make an effort to spend time with them and use their hobbies and interests as a guide for your actions together? Did you do what you could to make your partner feel appreciated?
These are all things you should consider before moving on and into another relationship, but remember not to turn this into a self-pity party. Your relationships may not always be what you intended, but they are always learning experiences that help you develop.
What event(s) caused the split?
Again, it's easy enough to define the cause if it's something like cheating that's quite discernable, but what about when it's not? Some people break off their relations because there's an underlying issue they don't want to discuss, or sometimes can't communicate with their partner. Maybe it's the fact that their partner is consistently messy and never cleans up after themselves, maybe there's bad and/or not enough sex, maybe they have an old ex that decided to show up in their life again, and they're feeling re-attached and don't want to cheat.
You can't always know why your partner might distance themself or break things off, but in most cases, once the relationship ends, you find out the reason. Just like finding who is to blame, evaluating the events that led up to the ending is also vital.
If you're the one that got dumped, and you did something wrong, and you weren't lucky enough to get a second chance, try your best to analyze the situation from their side. If your partner had done the same thing you did to them, would you put up with it? More importantly, in your next relationship, are you going to make the same mistake again? As mentioned above, learning where you went wrong and what you did specifically will help you avoid it in the future.
Let's say you're the one who did the dumping. Why'd you do it? Could you have communicated about the issue before just breaking it off if the relationship was worth saving? Knowing what that person did wrong will help you avoid it in the future. For example, if your partner drank too much, and was consistently drunk, picking someone that isn't interested in drinking or doesn't drink at all can help circumvent that issue entirely. If it's something less-obvious, like bad sex or a lack of them showing appreciation towards you, you NEED to communicate it in your next relationship.
How is the next person you spend your time with going to know how to keep you happy if you don't tell them what needs work? How would you know what YOU want in the next relationship, if you don't look back on your previous ones to determine what went wrong?
One of the most important things to remember about relationships in general, is that they are a constant source of self-improvement. Even if it ends, even if it was a sour ending, you can still take away something that will make you more successful the next time around. Sometimes it's an improvement to your communication skills, sometimes it's an extra boost of confidence, sometimes it was some much-needed sex advice. Everyone has to learn at their own pace, their own way. You don't wake up overnight and suddenly be the best partner ever for the rest of your life.
Taking a breakup full of anger and sadness and possible hatred, and turning it into a learning experience is a massive step in the right direction. Focusing your efforts and time on improving yourself, rather than beating yourself up over it, will also do wonders for your mood.
Remember that you are worth something. So what if your relationship ended? The person you were with was still initially with you for a reason. Sometimes people don't find their perfect relationship until their 40+ years old, and even then they're STILL learning. Humans are complex, and relationships even more so. You won't master every aspect of them in a single experience, probably not even several.
Expect some breakups, expect some disasters, but learn from them. Take what you've experienced and make your life and possible future relationships better with it.